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GraphicalModels :: globalMarkov

globalMarkov -- Global Markov statements for a directed graph.

Synopsis

Description

Given a directed graph G, global Markov states that A is independent of B given C for every triple of sets of vertices A, B, and C, such that A and B are d-separated by C (in the graph G).

The global independent statements are computed using the Bayes ball algorithm, as described in the paper "Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)" by Ross D. Shachter.

For example, for the digraph D on 4 vertices with edges a->b, a->c, b->c, and b->d, we get the following global Markov statements:
i1 : D = digraph {{a,{b,c}}, {b,{c,d}}, {c,{}}, {d,{}}}

o1 = Digraph{a => set {b, c}}
             b => set {c, d}
             c => set {}
             d => set {}

o1 : Digraph
i2 : L = globalMarkov D

o2 = {{{a, c}, {d}, {b}}}

o2 : List
Note that the method displays only non-redundant statements.

Caveat

See also

  • localMarkov -- Local Markov statements for a directed graph.
  • pairMarkov -- Pairwise Markov statements for a directed graph.

Ways to use globalMarkov :

  • globalMarkov(Digraph)